In this section, we will use the circle method from [1]} to count zeros of diagonal quadratic forms in four variables, the main goal being the proof of Theorem REF . Before proceeding with the proof, we collect together some of the notation which we will use throughout this section. Much of the notation depends on a vector \(\mathbf {a}= (a_1,\ldots ,a_4) \in (\mathbb {Z}_{\ne 0})^4\) , which remains fixed throughout this section.
